Question

Write the equation x^2 + 7y^2 - 12x - 13 in standard form. State which type of conic section it is.

Please Help Medals will be given.

Answer 1

Given x^2 + 7y^2 - 12x - 13
Both the x^2 and y^2 are present so it is ellipse or hyperbola
The sign of the coefficients are the same so it is an ellipse.
Complete the square on the x and on the y terms.
x^2-12x +36 + 7(y^2) = 13+36
Factor:
(x-6)^2 + 7(y-0)^2 = 49
Standardize
(x-6)^2/7^2+(y-0)^2/(sqrt(7))^2 = 1
Center: (6,0)
Semi major axis: 7 (horizontal)

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